We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.

翻译：本文提出一种新型图变换器框架HAMLET，旨在解决使用神经网络求解偏微分方程（PDEs）时面临的挑战。该框架采用具备模块化输入编码器的图变换器，将微分方程信息直接融入求解过程。这种模块化设计增强了参数对应控制能力，使HAMLET能够适应任意几何构型及多种输入格式的PDEs。值得注意的是，HAMLET在数据复杂度与噪声水平增加时仍能保持有效缩放，展现出强鲁棒性。该框架不仅适用于单一类型的物理仿真，还可跨领域应用。此外，在数据稀缺场景下，HAMLET尤其能提升模型稳健性与性能。通过大量实验证明，本框架在PDEs求解能力上优于现有技术。